Given the matrices A and B below, transform the compound matrices [A I] and [B I] (where I is the identity matrix of size 3 X 3), into matrices in reduced row echelon form and use them to determine whether A and B have inverses. If they do, find them. Do not use MATLAB.
A =
1 2 -1
2 2 4
1 3 -3
B =
2 1 -4
-4 -1 6
-2 2 -2
Answers
the inverse of B, we look at the right side of [B I] in reduced row echelon form, which is [ -1/3 1/3 2/3].
What is Matrix?A matrix with m rows and n columns is called an m-by-n matrix or simply an m×n matrix. The order of a matrix refers to its dimensions, i.e., the number of rows and columns, and is typically written as m×n. Matrices can be added, subtracted, multiplied, and transformed using various algebraic operations.
Given by the question.
We start by forming the augmented matrices [A I] and [B I]:
Now we apply row operations to both matrices to transform them into reduced row echelon form:
In reduced row echelon form, the identity matrix is always on the left side of the augmented matrix. We can see that both [A I] and [B I] have reduced row echelon form with the identity matrix on the left side. This means that both A and B are invertible.
To find the inverse of A, we look at the right side of [A I] in reduced row echelon form, which is [ -2 1 2 ]. This means that:
\(A^{-1}\) = \(\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]\)\(\left[\begin{array}{ccc}-2&1&2\\1&-1/2&-1/2\\-1/3&1/3&1/3\end{array}\right]\)
To find the inverse of B, we look at the right side of [B I] in reduced row echelon form, which is [ -1/3 1/3 2/3 ]. This means that:
\(B^{-1}\)=\(\left[\begin{array}{ccc}-1/3&1/3&2/3\\2/3&-1/3&-1/3\\-1/3&1/3&1/3\end{array}\right]\)
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Related Questions
Which is the best estimate for the product of 59 × 3 . 7 ? A. 18 B. 24 C. 180 D. 240
Answers
Answer:
D. 240
Step-by-step explanation:
estimate means round off
59 becomes 60
3.7 becomes 4
60 x 4 is 240
So the closest is 2:40
Max measures the angles in a triangle.
He says the angles are 50°, 35º and 85°,
Explain why Max cannot be correct.
Answers
Answer:
Max cannot be correct because a triangle is made up of three angles, whose sum is 180°. Max's answers add up to 170°
Please Help.... 50 points.
Answers
Answer:
94
Step-by-step explanation:
Answer:
94 is the answer
Step-by-step explanation:
A company discovers that to produce x = 940 new electronic parts, it will cost y = $55040. To produce 1000 new electronic parts, it will cost $58100.
Compute the slope of the costs and choose the most accurate statement from the following:
A.) Costs are increasing at a rate of $57 per item.
B.) Costs are decreasing at a rate of $50 per item.
C.) Costs are decreasing at a rate of $57 per item
D.) Costs are increasing at a rate of $51 per item.
E.) Costs are decreasing at a rate of $51 per item.
F.) Costs are increasing at a rate of $50 per item.
Answers
The slope of the costs and choose the most accurate statement are captured in the below option:
D.) Costs are increasing at a rate of $51 per item
What is the slope cost?
The slope of a line is the degree of change in y coordinates(costs) with respect to change in x coordinates(volume of output).
The formula for slope of the costs is as given below:
slope=(new costs-old costs)/(new quantity-old quantity)
new costs=$58,100
old costs=$55,040
new quantity=1000
old quantity=940
slope=($58,100-$55,040)/(1000-940)
slope=$51.00
This implies that for every additional new electronic part, the cost goes up by $51.00
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Y’all got on Brainly quick it’s only Wednesday
Answers
Answer:
some ppl got summer school
Step-by-step explanation:
3. If a 35-foot cable were run from the top of the pole and anchored to the ground at a distance from the pole, about how far away from the pole would it be anchored?
Answers
The distance from the pole at which the cable is anchored is about 25 feet from the pole .
Given that a 35-foot cable is run from the top of the pole and anchored to the ground at a distance from the pole. The problem is to determine about how far away from the pole would it be anchored.
Let AB be the pole of length 40 feet, and CD be the 35-foot long cable anchored to the ground at D and attached to the top of the pole at C. Let E be the point on the ground at which the cable is taut and is anchored. The distance ED is to be determined.
we can see that ∆CDE is a right-angled triangle with ∠CED = 90°.
Using Pythagoras Theorem, we have:CD² = CE² + DE²35² = (40 - ED)² + DE² .
Simplifying the above equation
1225 = 1600 - 80ED + ED²
1225 - 1600 + 80ED - ED² = 0ED² - 80ED + 375 = 0
Factorizing the above quadratic equation
ED² - 25ED - 15ED + 375 = 0ED(ED - 25) - 15(ED - 25)
= 0(ED - 15)(ED - 25) = 0So, ED = 15 ft or ED = 25 ft.
The negative value of ED is extraneous since it represents a point below the ground, which is not possible. Therefore, the distance from the pole at which the cable is anchored is about 25 feet from the pole.
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What are the approximate solutions of the graphed function?
Answers
Answer:
x = -2.6, x = 2.6
Step-by-step explanation:
The graph crosses the x-axis at approximately 2.6 and -2.6.
The required approximate solution of the function graphed is x = -2.6 and 2.6.
Given that,
A graph of a function is plotted, and the solution of the function is to be determined.
What are functions?
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
What is a graph?The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here, the solution of the function is that value of x where the function terminates to zero, So the given curve terminates to zero at two places at x = -2.6 and x = 2.6 from the observation of the graph.
Thus, the required approximate solution of the function graphed is x = -2.6 and 2.6.
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solve the equation 2x^3 + 24x^2 =56x
Answers
Answer:
2x(x^2+24x-28).
Step-by-step explanation:
2x^3+24x^2=56x.
2x(x^2+12x+28x).
I think that's the answer.
Paperback books sell for $5.95 normally. The book shelf offers them for 15% off. How much do you save? What is the price of a paperback book at the book shelf?
Answers
Answer:
Use the given functions to set up and simplify
15
%
.
5.95
=
15
%
=
0.15
2 cars departed the same place at the same
time. They traveled the same direction. One
traveled 50 mph for 4 hours. The other car
traveled 60 mph for 8 hours. How many miles
farther did the 2nd car travel?
Answers
Mary is driving on a highway. She uses one gallon of gas for every 50 miles she drives. The distance, D (in miles), she travels on g gallons of gas is given by the following function.
D (g) = 50g
How far does Mary drive if she uses 5 gallons of gas?
Answers
In order to receive this answer you multiply 50 by 5,and you get 250.
I hope this helps:)
If you have any questions about my answer please feel free to ask:)
find the solution set of x² - 7x = -12?
a. {-2, 4}
b. {-4, 1}
c. {4, -4}
d. {3,4}
Answers
Answer:
The answer is d.
Step-by-step explanation:
\(x^{2} -7x+12=0\\(x-3)(x-4)=0\\x-3=0; x=3\\x-4=0; x=4\\(3,4)\)
How do i solve it with steps pls
Answers
Answer:
Step-by-step explanation:
We know the the total of angles for a triangle is 180 degrees.
So in this case we'd want to set up adding all of our angles and setting them equal to 180
17 + 126 + b = 180
then solve for b
143 + b = 180
b = 37 degrees
So the answer would be 37 degrees for angle b
A restaurant has a rectangular patio section that is 8 meters wide by 6 meters long. They want to use fencing to enclose the patio.
How much fencing will they need to go around their new patio?
meters
Answers
308
This is the answer
The restaurant will need 28 meters of fencing to enclose their new patio.
Here, we have to calculate the amount of fencing needed to enclose the rectangular patio, we need to find the perimeter of the patio.
The perimeter of a rectangle is the sum of all its sides.
Given:
Width (W) = 8 meters
Length (L) = 6 meters
The formula for the perimeter (P) of a rectangle is:
P = 2 * (Width + Length)
Plug in the values:
P = 2 * (8 meters + 6 meters)
P = 2 * 14 meters
P = 28 meters
So, the restaurant will need 28 meters of fencing to enclose their new patio.
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Place parentheses in the expression so that it equals the given value.
20 + 2 x 5 + 4^1
Value: 38
Answers
What is the number of 20% of 40
Answers
Answer:
8
Step-by-step explanation:
40 x 0.20
= 8
Given f (x) = 3x - 6 and g (x) = 2x²
1. Find: f (g (x))
2. Evaluate: f ( g ( -2))
PLEASE HELP ASAP!
Answers
Answer:
1. 6x^2-6
2. 18
Step-by-step explanation:
1. f(g(x))= 3(2x^2)-6= 6x^2-6
2. f(g(-2))= 3 (2(-2)^2)-6= 3(2(4))-6= 3(8)-6=24-6=18
2. 18
Have a nice day / night! :)
What ordered pairs are the solutions of the system of equations shown in the graph below?
Answers
Answer:
(4,0) & (9,5)
Step-by-step explanation:
Where the equations cross are the solutions!
Hope this Helps! :)
Happy Studies
Find the value of x that makes mll n.
150°
(3x-15)
Answers
Answer:
\(3x - 15 = 150 \\ 3x = 165 \\ x = 55\)
55° is the right answer.There were 630 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $950. How many adults and how many children attended?
Answers
Answer:
315 adults and and 215 children
Step-by-step explanation:
"If 54 oranges costs find the cost - Of 3 I
oranges
Answers
Answer:
Step-by-step explanation:
Cost of 3 oranges = cost of 54 oranges / 18
Same set up as the problem to the left. Fill in the blanks.
Answers
The blanks that are missing in the sequence are -3 and 11
How to fil in the blanks in the sequencefrom the question, we have the following parameters that can be used in our computation:
The blanks in the sequence
When listed out, we have
_, _, 25, 39
Assuming that the sequence, is an arithmetic sequence, then we have
Common difference = 39 - 25
Common difference = 14
This means that
Previous term = 25 - 14 = 11
Firs term = 11 - 14 = -3
So, the missing terms are -3 and 11
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Looking at the picture below, what are two things that you would correct about this student's posture and playing position if you were the teacher.
Please answer ASAP
Answers
Answer:
The Student has good posture on the chin rest but The way that there are not standing straight up and how there holding the bow is incorrect
Step-by-step explanation:
Sitting up straight, turn your head enough that your nose lines up with the left foot. Drop your chin and place the violin so that it's also aligned with your left foot. Hold your spine straight and relax into this position; you should be able to keep the violin steady using only your chin.
I'm not 100 percent sure this correct
I need help with the second part
Answers
The probability that each bill is a $1 bill is given as follows:
1/16.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
The bills are replaced, hence we consider that for each trial, there is a 1/4 probability of selecting a $1 bill, as one out of the four bills are of $1.
Hence the probability that each bill is a $1 bill is obtained as follows:
p = 1/4 x 1/4
p = 1/16.
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A light bulb manufacturer claims that a certain type of bulb they make has a mean lifetime of 100010001000 hours and a standard deviation of 202020 hours. Each package sold contains 444 of these bulbs. Suppose that each package represents an SRS of bulbs, and we calculate the sample mean lifetime \bar x
x
ˉ
x, with, \bar, on top of the bulbs in each package.
Answers
The null and alternative hypotheses are H0: µ ≥ 1000 and Ha: µ < 1000 respectively.
The evidence to reject the manufacturer's claim is in the rejection region for the test statistic which is z < -1.54.
What is the null and alternative hypothesis?The null hypothesis consist of the inequality sign “equal” sign (“=” or “≥” or “≤”).
Alternative hypothesis is the complement to the null hypothesis.
The claim: The mean life of a certain type of light bulb is at least 1000 hours”. At least in inequality is represented by “≥” sign, it is null hypothesis.
H0: µ ≥ 1000
Alternative hypothesis:
The alternative hypothesis is the complement, that is, the mean life of a certain type of light bulb is less than 1000 hours.
Ha: µ < 1000
As the alternative hypothesis contains “<” sign, the test is left-tailed.
Using α = 0.02, we have critical value from standard table of normal distribution:
z0 = -1.54
Therefore, the rejection region for the test statistic is z < -1.54.
Complete question:
A light bulb manufacturer claims that a certain type of bulb they make has a mean lifetime of 1000 hours and a standard deviation of 20 hours. Each package sold contains 4 of these bulbs. Suppose that each package represents an SRS of bulbs, and we calculate the sample mean lifetime \bar x x ˉ x, with, \bar, on top of the bulbs in each package. 1. What is the null and alternative hypotheses? 2. At a = .02, do you have enough evidence to reject the manufacturer's claim?
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Levy is painting a miniature model of a World War II tank. His figure uses a 1:72 scale and is 22.5 cm
long. How many centimeters long was the actual tank?
cm
Answers
Levy is painting a miniature model of a World War II tank. His figure uses a 1:72 scale and is 22.5 cm long. The actual tank is 1620 cm long.
To determine the length of the actual tank, we need to scale up the length of the miniature model using the given scale of 1:72.
Let's denote the length of the actual tank as "x".
According to the scale, 1 cm on the miniature model represents 72 cm on the actual tank.
So, we can set up the following proportion:
1 cm (miniature model) / 72 cm (actual tank) = 22.5 cm (miniature model) / x cm (actual tank)
Cross-multiplying and solving for x, we get:
x = (72 cm * 22.5 cm) / 1 cmx = 1620 cm
The actual tank is 1620 cm long.
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sketch the region y=sqrtx, y=0, x=4
Answers
Answer:
see attached for a sketch
area = 5 1/3 square units
Step-by-step explanation:
You want the area under the square root curve, above y=0, from x=0 to x=4.
AreaThe area is found by integrating a differential of area over appropriate limits. A vertical slice will have hight √x and width dx, so we have ...
dA = (√x)dx
A = ∫(√x)dx
The power rule can be used for the integration:
\(\displaystyle A=\int_0^4{x^{\frac{1}{2}}}\,dx=\left[\dfrac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]^4_0=\dfrac{2}{3}(4^\frac{3}{2})=\dfrac{16}{3}=\boxed{5\dfrac{1}{3}}\)
The area of the region is 5 1/3 square units.
__
Additional comment
You will notice that the area is bounded by a rectangle 4 units wide and 2 units high, for an area of 4·2 = 8. The area under the parabolic curve is 2/3 of that: 2/3·8 = 16/3 = 5 1/3 square units.
This fraction will be true for any area bounded by a parabola where the vertex is one of the corners of the rectangle.
#95141404393
$13,000 was borrowed from two sources, one that charges 15% simple interest and the other that charges 10% simple interest. If the total interest at the end of 1 year was $1750, how much money was borrowed from each source?
Answers
9514 1404 393
Answer:
$9,000 at 15%$4,000 at 10%Step-by-step explanation:
Let x represent the amount borrowed at 15%. Then the amount borrowed at 10% is (13000-x). The interest at the end of the year is ...
0.15(x) + 0.10(13000 -x) = 1750
0.05x = 1750 -1300 . . . . . . . . . . . . simplify, subtract 1300
x = 450(20) = 9000 . . . . . . . . . . multiply by 20
$9,000 was borrowed at 15%; $4,000 was borrowed at 10%.
give two ways to write the expression as a phase for n+6
Answers
1. N plus 6
2. A number n is added to 6
Adrian made a cone from construction paper. the equation for the surface area of a cone is a=pi r^(2)+pi rs, where r is the radius of the base and s is slant height of the cone. dimensions of the cone are h=,8 ; r=,3
what is the total of paper needed?
Answers
The total amount of paper required is 3π(3+√71)unit²
The equation for the surface area of a cone is given as follows:
A = πr²+πrs.
Height of the cone, h = 8 & radius of the cone = 3, the slant height s is given as: s = √(r²+h²)
Substituting the values of r & h to determine s
s = √(8²+3²)
s = √71
Substituting the values to get Area,
A=π*3²+π*3*√71.
A=3π(3+√71)
Hence, the required paper will be A=3π(3+√71)unit²
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